The wide receiver has agreed a deal worth up to $43m (£28.8m), having previously signed a one-year restricted free agent tender.
The 26-year-old told the team's official website: "I feel relief. I feel I can just kick back and play football again.
"This is just another step to getting where I want to be at the end of my career, I love to do well for my team and do well each and every year and continue to prove myself and not feel complacent and not feel I've done enough.
"I want to continue to have catches and yards and touchdowns and help my team win and get to the playoffs and get to the Super Bowl. To do that in such an early part of my career was outstanding, but you want more, you want to continue to feel that."
Cruz had 1,092 receiving yards and 10 touchdowns for the Giants last season.